The caching problem has been extensively studied in the literature under different assumptions on the request process. When the requests occur according to a given stochastic process,
the analysis leads usually to complex formulas even in simple settings. For example, even the hit ratio of a single cache managed by the LRU eviction policy under the independent reference model is hard to precisely characterize [1]}, [2]}.
The characteristic time approximation (often referred to as Che's approximation) significantly simplifies this analysis by assuming that a file, in absence of additional requests for it, stays in the cache for a random time sampled independently from requests for other files. First proposed by Fagin [3]} and later rediscovered and popularized by Che et al
 [4]}, the approximation has been justified formally by several works  [5]}, [6]}, [7]}
and has allowed the study of a large number of existing [8]} and new [9]}, [10]} caching policies. It also applies to networked settings [11]}, [12]}, [13]}, [14]}
and to more general utilities beyond the hit ratio [15]}, [16]}, all under stochastic requests.
